5 
To the determination of the closure error the procedure is the following: 
1. °—The ground coordinates (M, N) of the points of the first model are trans 
formed in autograph coordinates by means of a Helmert transformation by 
using the control points of the first model. 
Thus, the transformation parameters DXo, DYo, DAZo and DXo are de 
termined. 
2. °—With these elements the ground coordinates (MnG, PnG), of the baricenter 
of the points of the last model are transformed. 
Let X’nG, Y’nG be the transformed coordinates of its baricenter. 
3. °— The ground coordinates (M, N) of the points of the last model are transformed 
in autograph coordinates (X, Y) by means of a second Helmert transforma 
tion. The control points of the last model are now used. 
The transformation parameters will be DAzn and DXn. 
4. °— The closure errors are calculated: 
Dx — XnG —X’nG 
Dy =YnG —Y’nG 
DAz = DAzn - DAzo 
DXn —DXo 
DfB = 
DXo 
where XnG and YnG are the autograph coordinates of the baricenter of the 
points of the last model. 
The expressions (Vermeir) utilized in the distribution of the closure errors are: 
AX(i), Ay{i)=f 1 (i) xBx (DfB, DAz)+f 2 {i) x (Dx, Dy) 
A/B(i), AAz(i)=f 3 (i) x (D(3, DAz) +/ 4 (*) x x {Dx, Dy) 
B 
with 
fi = 
/ 2 = 
fs = 
i(i+ 1) (n-i) (n+ 1) 
n 3 — n 
i(i+ 1) (2i-3n +1) 
n 3 — n 
(2n+ l)i—3i 2 
n 2 — n 
i 2 — ni 
n A — n